How to create such a mechanism?
You can get this effect by using a cast modifier and instancing. Create a plane and use edge loops and cut once down the middle and a few times on the side. Then delete everything besides the middle edges to create a single line of vertices. Then in the object properties for it, set instancing to vertices and add a cast modifier. Then create the rectangles or whatever else you want to be moving up and down. Then set the relations for its object properties to be the line of verts you previously made. This should instance the rectangle to all the verts on the line.
Now create an empty, and in the cast modifier settings you added to the line, set the object to be the empty. Make sure to clamp it to the Z axis as well in the modifier settings. Mess with the scale and radius settings until you get the effect you want.